I think this has to do with how the phi ($\phi$) is calculated and reported by the software you use. Let's use an example and assume that we have a small data set with two dichotomous variables (0=no, 1=yes):
ss <- c(0,0,1,0,0,1,1,0,1,0)
ms <- c(1,1,0,1,0,1,0,1,0,1)
And we want to calculate the Pearson's correlation ($r$) using this formula:
$$r = \frac{\sum(x_i - \bar x)(y_i - \bar y)}{\sqrt{\sum(x_i-\bar x)^2 \sum(y_i-\bar y)^2}}$$
You can plug the numbers into the formula or simply run the function cor in R:
cor(ss, ms)
-0.5833333
As in your case, we have a negative $r$. Now, we can calculate $\phi$ for $2 \times 2$ contingency table using our two variables:
| | ms | |
|-----|----|-----|
| ss | no | yes |
| no | 1 | 5 |
| yes | 3 | 1 |
We can use the formula on this wikipedia page for $\phi$ coefficient. Let's assign letters to make it simple, and then plug the numbers:
| | ms | |
|-----|----|-----|
| ss | no | yes |
| no | A | B |
| yes | C | D |
$$\phi = \frac{AD-BC}{\sqrt{(A+B)(C+D)(A+C)(B+D)}} = \frac{1-15}{\sqrt{6 \times 4 \times 4 \times 6}} = -0.5833333$$
Exactly the same result. So, why do you have a positive value then? If you google around, you can see a different formula for $\phi$:
$$\phi = \sqrt{\frac{\chi^2}{N}}$$
In fact, this is the formula of Cramér's V (sometimes called Cramér's phi, $\phi_c$) simplified for $2 \times 2$ contingency tables. These two measures are related: "In the case of a $2 \times 2$ contingency table Cramér's V is equal to the absolute value of Phi coefficient." We can check this using our small data, where $\chi^2 \approx 3.403$
$$\phi_c = \sqrt{\frac{3.403}{10}} \approx 0.583 $$
This could explain why you observe a reversal of sign.
